Preston Wake

Pseudo-modularity and Iwasawa theory

Abstract:We prove, assuming Greenbergs conjecture, that the ordinary eigencurve is Gorenstein at an intersection point between the Eisenstein family and the cuspidal locus. As a corollary, we obtain new results on Sharifis conjecture. This result is achieved by constructing a universal ordinary pseudodeformation ring and proving an

Full level structures revisited: pairs of roots of unity

R=\Bbb{T}

Eisenstein Hecke algebras and conjectures in Iwasawa theory

result.

Hecke algebras associated to Λ-adic modular forms

Abstract We introduce a notion of full level structure for the group scheme ( μ p × μ p ) / Z , and show that scheme of full level structures is flat over Z .

Ordinary pseudorepresentations and modular forms

We formulate a weak Gorenstein property for the Eisenstein component of the p-adic Hecke algebra associated to modular forms. We show that this weak Gorenstein property holds if and only if a weak form of Sharifis conjecture and a weak form of Greenbergs conjecture hold.